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Probability for Finance

Probability for Finance
4.9 (13 reviews) Read reviews
ISBN: 978-87-7681-589-9
1 edition
Pages : 115
Price: Free

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Summary

This book provides technical support for students in finance.

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About the book

  1. Description
  2. Content
  3. About the Author
  4. Embed
  5. Reviews

Description

This book provides technical support for students in finance. It reviews the main probabilistic tools used in financial models in a pedagogical way, starting from simple concepts like random variables and tribes and going to more sophisticated ones like conditional expectations and limit theorems. Many illustrations are given, taken from the financial literature. The book is also a prerequisite for “Stochastic Processes for Finance” published in the same collection.

Content

Introduction

1. Probability spaces and random variables
1.1 Measurable spaces and probability measures
1.1.1 σ algebra (or tribe) on a set Ω
1.1.2 Sub-tribes of A
1.1.3 Probability measures
1.2 Conditional probability and Bayes theorem
1.2.1 Independant events and independant tribes
1.2.2 Conditional probability measures
1.2.3 Bayes theorem
1.3 Random variables and probability distributions
1.3.1 Random variables and generated tribes
1.3.2 Independant random variables
1.3.3 Probability distributions and cumulative distributions
1.3.4 Discrete and continuous random variables
1.3.5 Transformations of random variables

2. Moments of a random variable
2.1 Mathematical expectation
2.1.1 Expectations of discrete and continous random variables
2.1.2 Expectation: the general case
2.1.3 Illustration: Jensen’s inequality and Saint-Peterburg paradox
2.2 Variance and higher moments
2.2.1 Second-order moments
2.2.2 Skewness and kurtosis
2.3 The vector space of random variables
2.3.1 Almost surely equal random variables
2.3.2 The space L1 (Ω, A, P)
2.3.3 The space L2 (Ω, A, P)
2.3.4 Covariance and correlation
2.4 Equivalent probabilities and Radon-Nikodym derivatives
2.4.1 Intuition
2.4.2 Radon Nikodym derivatives
2.5 Random vectors
2.5.1 Definitions
2.5.2 Application to portfolio choice

3. Usual probability distributions in financial models
3.1 Discrete distributions
3.1.1 Bernoulli distribution
3.1.2 Binomial distribution
3.1.3 Poisson distribution
3.2 Continuous distributions
3.2.1 Uniform distribution
3.2.2 Gaussian (normal) distribution
3.2.3 Log-normal distribution
3.3 Some other useful distributions
3.3.1 The X 2 distribution
3.3.2 The Student-t distribution
3.3.3 The Fisher-Snedecor distribution

4. Conditional expectations and Limit theorems
4.1 Conditional expectations
4.1.1 Introductive example
4.1.2 Conditional distributions
4.1.3 Conditional expectation with respect to an event
4.1.4 Conditional expectation with respect to a random variable
4.1.5 Conditional expectation with respect to a substribe
4.2 Geometric interpretation in L2 (Ω, A, P)
4.2.1 Introductive example
4.2.2 Conditional expectation as a projection in L2
4.3 Properties of conditional expectations
4.3.1 The Gaussian vector case
4.4 The law of large numbers and the central limit theorem
4.4.1 Stochastic Covergences
4.4.2 Law of large numbers
4.4.3 Central limit theorem

Bibliography

About the Author

Patrick Roger is a professor of Finance at EM Strasbourg Business School, University of Strasbourg. He mainly teaches Derivatives, Investments, Behavioral Finance and taught Financial mathematics for more than 20 years at University Paris-Dauphine. As a member of LaRGE Research Center, he wrote more than 15 books and 50 research papers in different areas of finance.

Author website: Click here.

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Reviews

Financial Engineering Student ★★★★☆

Very well written with the right balance between concepts and applications. It is aptly named as probability for finance and is a very good primer for people who want to progress to advanced topics in mathematical finance. There were many gaps in my knowledge acquired during my masters in financial engineering and the author does a good job not only in explaining the concepts but also the need for these mathematical tools. Highly rated.